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April 16, 2014

Homework Help: Math: Calculus

Recent Homework Questions About Calculus

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Calculus
Find the area cut off by x=4 from the hyperbola x^2/9-y^2/4=1. Answer is 4.982 in the book. I have proceeded as under: Y=2/3*sqrt(x^2-9) and rhe reqd. area is double of integral 2/3*sqrt(x^2-9) from 3 to 4. Int= 2/3*[xsqrt(x^2-9)/2 – 9/2*log{x+sqrt(x^2-9)}] from 3 to 4 =x...
Friday, March 28, 2014 at 2:17am

Calculus Help Please!!!
One of us made an arithmetic mistake. It is up to Tanya to get it right :)
Thursday, March 27, 2014 at 9:06pm

Calculus Help Please!!!
According to Newton's Law of Cooling T(t) = roomtemp + (37 - 20)e^(-kt) , where t is the time in hours and k is a constant so we get two equations: 32.5 = 20 + 17e^(-kt) ---> 12.5 = 17e^(-kt) and 30.3 = 20 + 17e^(-k(t+1)) ---> 10.3 = 17e^(-kt - k) divide them: 115/...
Thursday, March 27, 2014 at 9:02pm

Calculus Help Please!!!
rate of change of temp proportional to temp above room temp which is 20 to make it easy on the arithmetic define T' = real T - 20 dT'/dt = k (T') dT/T' = k dt ln T' = k t T' = C e^kt let's call t = 0 at 1:30 T = 32.5 so T' = 12.5 12.5 = C e^0 = ...
Thursday, March 27, 2014 at 8:54pm

Calculus Help Please!!!
I am going to assume it is algebra first take t = 0 at 1:30 T = Ti - k t Ti = 32.5 so T = 32.5 - k t 30.3 = 32.5 - k (1 hour) k = 2.2 so T = 32.5 - 2.2 t 37 = 32.5 - 2.2 t t = - 2.04 call it 2 hours so by that linear model 11:30 am now I will work on the more realistic ...
Thursday, March 27, 2014 at 8:38pm

Calculus Help Please!!!
Are you sure this is calculus? You want exponential decay to room temp? Or is it algebra and you want a linear function?
Thursday, March 27, 2014 at 8:30pm

Calculus Help Please!!!
In a murder investigation, the temperature of the corpse was 32.5 C at 1:30pm and 30.3 C an hour later. Normal body temperature is 37.0 C and the temperature of the surrounding was 20.0 C. When did the murder take place? PLEASE SHOW STEP BY STEP
Thursday, March 27, 2014 at 8:16pm

Calculus
best use radians, pi/2
Thursday, March 27, 2014 at 3:20pm

Calculus
when t=90?
Thursday, March 27, 2014 at 2:59pm

Calculus
y" = 5cos(t) so, when is that zero?
Thursday, March 27, 2014 at 2:52pm

Calculus
A weight oscillates in a vertical motion according to the position function y(t)=-5 cos(t). Assuming t≥0, when will the acceleration if the weight be zero for the first time?
Thursday, March 27, 2014 at 2:51pm

Calculus
-9.8 m/s^2
Thursday, March 27, 2014 at 2:45pm

Calculus
An object in free fall has its distance from the ground measured by the function d(t)=-4.9t^2 +50, where d is in meters and t is in seconds. If gravity is the only acceleration affecting the object, what is gravity's constant value?
Thursday, March 27, 2014 at 2:37pm

Calculus
Ahh. I see that I was interpreting 243^3/5 as (243^3)/5
Thursday, March 27, 2014 at 12:05pm

Calculus
just using ln a^b = b ln a ln (243^3/5 *32^4/5) = ln ( (3^5)^(3/5) * (2^5)^(4/5) ) = ln ( 3^3 * 2^4) = ln (27*16) = ln(432) 1/5 ln (243^3 * 32^4) = ln [ (243^3 * 32^4) ^(1/5) ] = ln (243^(3/5) * 32^(4/5) ) = .... = ln(432)
Thursday, March 27, 2014 at 12:01pm

Calculus
No one is bothered by the fact that 5 does not divide powers of 2 and 3?
Thursday, March 27, 2014 at 11:37am

Calculus
same as y": -cosx
Thursday, March 27, 2014 at 11:25am

Calculus
If y=cos x, what is y^(6) (x)?
Thursday, March 27, 2014 at 11:18am

Calculus
I agree with Damon's "huh" since ln (243^3/5 *32^4/5) = 1/5 ln (243^3 * 32^4)
Thursday, March 27, 2014 at 10:30am

CALCULUS problem
int x^-3 dx = -.5 x^-2 + c at x = 3 = -.5/9 at x = 1 = -.5 so A = .5 - .5/9 = .5(8/9) = 4/9 B at x = h int = -.5/h^2 right half = -.5/9 +.5/h^2 left half = -.5 h^2 +.5 so -.5 h^2 + .5 = -5/9 +.5/h^2 1/h^2 = .5 + 5/9 = 4.5/9 + 5/9 = 9.5/9 = 19/18 int 1 to 3 of pi (x^-6)dx = -pi...
Thursday, March 27, 2014 at 9:53am

CALCULUS problem
There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region R is bounded by the x-axis, x = 1, x = 3...
Thursday, March 27, 2014 at 8:51am

Calculus
huh?
Thursday, March 27, 2014 at 7:51am

Calculus
good except for this step: ln (243^3/5 *32^4/5) should be 1/5 ln (243^3 * 32^4)
Thursday, March 27, 2014 at 5:36am

Calculus
The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00 at time t hours after 12:00, (at t=0) the minute hand is at 4.5 sin(2pi*t) the hour hand is at 2.0sin(2pi*t/12) at 9:00, the distance d is d^2...
Thursday, March 27, 2014 at 5:34am

Calculus
x = ln 243 y = ln 32 LET Z = e^((3x + 4y)/5) ln [z ]= (3x+4y)/5 ln z = (1/5)( 3 ln 243 + 4 ln 32) = ln (243^3/5 *32^4/5) = ln (27*16) = ln(432) if ln z = ln 432 then z = 432
Thursday, March 27, 2014 at 3:54am

Calculus
Posted by MG on Wednesday, March 26, 2014 at 6:54pm. The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at ...
Thursday, March 27, 2014 at 3:36am

Calculus
If e^x = 243 and e^y = 32 then e^((3x + 4y)/5) =? The answer is 432, but I don't understand why.
Thursday, March 27, 2014 at 3:34am

College Calculus
Thank you for the response, i tried the method mentioned above three times and was incorrect each time, i double checked all my work to match the method above. The correct answer is always just .3 under the answer All of your arithmetic is right as well, so it is not that. ...
Thursday, March 27, 2014 at 3:31am

pre calculus
C(x) = 2.00 for 0 < x <= 1 2.00 + .20(10x) for 1 < x < 2 since there are 10 charging units per mile.
Thursday, March 27, 2014 at 12:10am

pre calculus
A taxi company charges $2.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 < x < 2
Thursday, March 27, 2014 at 12:07am

Calculus
Thank you very much!
Wednesday, March 26, 2014 at 11:46pm

Pre calculus
yes. The reason the law of sines can give two triangles is because sin(x) is positive all the way from 0 to 180. cos(x) becomes negative for x>90, so the formula takes that into account, always leaving only one possible answer. I mean, think about it geometrically. If you ...
Wednesday, March 26, 2014 at 11:46pm

Calculus
Since velocity is the derivative of position, v(t) = -32t + 160 now just solve -32t+160 = 32 -32t+128 = 0 t = 4
Wednesday, March 26, 2014 at 11:39pm

Calculus
The height in feet above the ground of a ball thrown upwards from the top of a building is given by s=-16t^2 + 160t + 200, where t is the time in seconds. If the maximum height is 600 feet, what is v^-1(32)? The answer is supposed to be 4 seconds, but I don't understand ...
Wednesday, March 26, 2014 at 11:07pm

argggh - Calculus
messed up in my expansion volume should have been 4x^3- 120x^2 + 800x and V' = 12x^2 - 240x + 800 = 0 3x^2 - 60x + 200=0 to get x = 4.23
Wednesday, March 26, 2014 at 10:11pm

Calculus
First things first: width --- s length ---- 2s 2s^2 = 800 s^2 = 400 s = 20 so the piece of metal is 20 by 40 let the side of the square to be cut out be x so the width is 20-2x the length is 40-2x the height is x Volume = x(20-2x)(40-2x) = 2x^3 - 120x^2 + 800x d(Volume)/dx = ...
Wednesday, March 26, 2014 at 10:05pm

Calculus
You are given a piece of sheet metal that is twice as long as it is wide an has an area of 800m^2. Find the dimensions of the rectangular box that would contain a max volume if it were constructed from this piece of metal by cutting out squares of equal area at all four ...
Wednesday, March 26, 2014 at 9:49pm

Calculus
you should have recalled that sin (-x) = -sinx so that sin(-.1) could not have been positive. did you mean -.1 ?
Wednesday, March 26, 2014 at 9:14pm

Calculus
Use a tangent line approximation at x=0 to estimate the value of sin(-0.1). I got 0.1
Wednesday, March 26, 2014 at 8:56pm

Calculus
yes v(t) = h ' (t) = -16t + 5 so v(0) = -16(0) + 5 = 5
Wednesday, March 26, 2014 at 8:54pm

Calculus
The vertical position of an object is modeled by the function h(t)=-16t^2 +5t+7, where h is measured in feet and t is measured in seconds. Find the object's initial velocity (that is, the velocity at t=0). Is it 5 feet per second?
Wednesday, March 26, 2014 at 8:46pm

Pre calculus
For the most part, will a law of cosines always be one triangle? As in one triangle to solve?
Wednesday, March 26, 2014 at 8:35pm

College Calculus
let Ø be the angle between them the angular velocity of the minute hand = 2π/60 rad/min = π/30 rad/min the angular velicity of the hour hand = 2π/(12(60)) or π/720 rad/min then, so dØ/dt = (π/30 - π/720) rad/min dØ/dt = 23&#...
Wednesday, March 26, 2014 at 8:25pm

College Calculus
I followed this example, where am i missing something or going about it wrong? If we let y be the angle between the two hands and x be the distance between the two tips, then, by the law of cosines, we have: x^2 = 5^2 + 1.5^2 - 2*5*1.5cos(y) x^2 = 27.5 - 15cos(y) Take the ...
Wednesday, March 26, 2014 at 6:58pm

College Calculus
The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at a rate of _______ m/hr at 9:00? I tried several times...
Wednesday, March 26, 2014 at 6:54pm

Calculus
dp/dt = v = 2 t at t = 2 v = 2*2 = 4
Wednesday, March 26, 2014 at 4:26pm

Calculus
If position is given by p(t)=t^2 +1, find the velocity v(t) at t = 2. I'm completely lost as to where to even start with this problem.
Wednesday, March 26, 2014 at 4:25pm

Calculus
I did one for you. Now you do this one. By the way you left the half life of carbon 14 or exponential decay function out of your statement of the problem making it impossible without looking that up.
Wednesday, March 26, 2014 at 10:38am

Calculus
12 = 40 e^(-kt) .3 = e^-30 k ln .3 = -30 k -1.20 = -30 k k = .04013 so .5 = e^-.04013 t -.6931 = -.04013 t t = 17.3 years
Wednesday, March 26, 2014 at 10:35am

Calculus
The amount of carbon-14 still present in a sample after t years is given by the function where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original carbon-14 level.
Wednesday, March 26, 2014 at 10:31am

Calculus
If 40 milligrams of strontium-90 radioactively decays to 12 milligrams in 30 years, find its half-life (the number of years it takes until half of it remains). Use the formula A = p ⋅ e−kt, where p is the amount and A the (smaller) final amount.
Wednesday, March 26, 2014 at 10:29am

calculus
A rectangular field is to be enclosed and divided into 4 equal lots by fences parallel to one of the sides. A total of 10,000 meters of fence are available. Find the area of the largest field that can be enclosed.
Wednesday, March 26, 2014 at 10:15am

pre calculus
-1 - 1/√3
Wednesday, March 26, 2014 at 5:45am

pre calculus
Find the exact values: tan(7pi/4) - tan (pi/6)
Wednesday, March 26, 2014 at 1:42am

Calculus
let the number be x, and the sum as stated be S S = x^2 + 1/x dS/dx = 2x - 1/x^2 = 0 for a max/min 2x = 1/x^2 2x^3 = 1 x^3 = 1/2 x = (1/2)^(1/3) or the cube root of 1/2
Tuesday, March 25, 2014 at 9:47pm

Calculus
Find a positive number such that the sum of the square of the number and its reciprocal is a minimum.
Tuesday, March 25, 2014 at 9:25pm

Grade 12 Calculus
thx!
Tuesday, March 25, 2014 at 9:14pm

Grade 12 Calculus
I hope your function looks something like this: R(x) = (5000 - 100x)(30 + x) = 150000+ 5000x - 3000x - 100x^2 = -100x^2 + 2000x + 150000 this is a standard parabola opening dowwards , so it will have a maximum the x of the vertex is -b/(2a) = -2000/-200 = 10 So there should be...
Tuesday, March 25, 2014 at 9:06pm

Grade 12 Calculus
For an outdoor concert, a ticket price of $30 typically attracts 5000 people. For each $1 increase in the ticket price, 100 fewer people will attend. The revenue, R, is the product of the number of people attending and the price per ticket. a) Let x represent the number of $1 ...
Tuesday, March 25, 2014 at 8:46pm

Calculus - good catch bob
Dang - forgot the restriction on the domain.
Tuesday, March 25, 2014 at 8:35pm

Calculus
now if you are allowed to remove trees, and for each tree removed, the average goes up by 5, then the optimal is to remove five trees.
Tuesday, March 25, 2014 at 8:29pm

Calculus
number apples=average*number trees let x be the nubmer of trees 50<x<inf number apples=(200-(x-50)*5)(x) where x is the number of trees, 50<x<infinity N=200x-5x^2 +250x dN/dx=0=200-10x+250 10x=450 x=45 but x>50, so look at optimal check x=50 N=50*200=10000 ...
Tuesday, March 25, 2014 at 8:28pm

Grade 12 Calculus
if the sheet is x by y, and is rolled along the y axis, 2x+2y = 100 v = pi r^2 y where 2pi r = x, or r = x/(2pi), so v = pi (x/(2pi))^2 (100-2x)/2 = x^2(50-x)/(4pi) dv/dx = x(100-3x)/(4pi) dv/dx=0 when x = 100/3 at that point, max v is pi*(50/3)^3
Tuesday, March 25, 2014 at 8:21pm

Calculus
the number of apples is yield/tree * # trees. With x trees, yield per tree is 200 - 5(x-50) for x > 50 So, total crop is c(x) = x(200-5(x-50)) = x(450-5x) = 450x - 5x^2 c'(x) = 450-10x c' = 0 at x=45 So, the max yield is achieved with 45 trees
Tuesday, March 25, 2014 at 8:16pm

Calculus
There are 50 apple trees in an orchard, and each tree produces an average of 200 apples each year. For each additional tree planted within the orchard, the average number of apples produced drops by 5. What is the optimal number of trees to plant in the orchard? I mostly need ...
Tuesday, March 25, 2014 at 8:09pm

Grade 12 Calculus
A rectangular piece of paper with perimeter 100 cm is to be rolled to form a cylindrical tube. Find the dimensions of the paper that will produce a tube with maximum volume. I have made it up to getting an equation for V(w).
Tuesday, March 25, 2014 at 7:49pm

Calculus Rate of Change
average=(finalvalue-initial value)/chngeinX final value= h'(6)=4*6=24 initial vealue=h'(2)=4*2=8 average h'=16/4=4 units unknown
Tuesday, March 25, 2014 at 10:52am

Calculus Rate of Change
Find the average rate of change h(x)=2x^2-4 from x=2 to x=6 Simplify your answer as much as possible
Tuesday, March 25, 2014 at 10:27am

calculus
v = 4π/3 r^3 v' = 4π r^2 at r=50, v = 500π/3 and v' = 100π So, the tangent line at r=50 is v - 500π/3 = 100π(x-50)
Tuesday, March 25, 2014 at 4:58am

Calculus
recall that the voulme of a sphare of radius r is v(r)=(4pir^3)/3. find l, ther linearisation of v(r) at r=50. A sphare of radius 50 centimeters is covered with a layer of point of thickness 0.31 millimeters. use the linearisation of v at r=50 to estimate the volume of point ...
Tuesday, March 25, 2014 at 2:13am

calculus
Recall that the volume of a sphere of radius r is V(r) =4\, \pi\, r^3 /3. Find L, the linearisation of V(r) at r=50
Tuesday, March 25, 2014 at 2:05am

Trigonometry
http://www.wolframalpha.com/input/?i=y%3​D2sin%28x-2pi%2F3%29 for x-intercepts, y = 0 2sin(x-2pi/3) = 0 sin(x-2pi/3)=0 but sin 0 = 0 and sin π =0 and sin 2π = 0 so x - 2π/3 = 0 and x -2π/3 = π and x - 2π/3 = 2π x = 2π/3 or x = &#...
Tuesday, March 25, 2014 at 12:11am

Calculus
fre
Monday, March 24, 2014 at 11:59pm

Calculus
x + 4xy = y^2 1 + 4y + 4xy' = 2yy' y' = (1+4y)/(2y-4x)
Monday, March 24, 2014 at 11:59pm

Calculus A
h' = (x^2-2x-9)/(x-1)^2 h" = 20/(x-1)^3 Clearly there are no inflection points, since f" is never zero h' is zero at two places, since the numerator is. So, there will be two extrema, one on each side of x=1. So, one will be a max, the other a min, depending ...
Monday, March 24, 2014 at 11:58pm

Calculus A
Find all relative extrema and points of inflection for the function; h(x)=(x^2+5x+4)/(x-1)
Monday, March 24, 2014 at 11:20pm

Calculus
Find dy/dx implicitly in terms of x and y only for the following function; x+ 4xy=y^2
Monday, March 24, 2014 at 11:17pm

Calculus
17
Monday, March 24, 2014 at 8:47pm

Calculus A
I will assume you meant: h(x) = x^2 + 5x + 4/(x-1) h ' (x) = 2x + 5 - 4/(x-1)^2 = 0 for max/min 2x + 5 = 4/(x-1)^2 (2x+5)(x^2 - 2x + 1) = 4 2x^3 - 4x^2 + 2x + 5x^2 - 10x + 5 = 4 2x^3 + x^2 - 8x + 1 = 0 hard to solve, Wolfram has this http://www.wolframalpha.com/input/?i=2x...
Monday, March 24, 2014 at 7:32pm

Calculus A
Find all relative extrema and points of inflection for the following function... h(X)= X^2+5X+4/ X-1 min= max= inflection points=
Monday, March 24, 2014 at 7:16pm

Calculus
Nevermind I didn't read the question correctly. I got it! Thank You!
Monday, March 24, 2014 at 1:43am

Calculus
after this, i am to solve the differential but I am confused as to what I would make T air. dT/dt=-k(45-Tair) what do i do with the other 2 variables since k is a constant of proportionality. and T air is a constant
Monday, March 24, 2014 at 12:49am

Calculus 12 Optimization
120
Sunday, March 23, 2014 at 9:35pm

calculus
Assuming an initial position of zero, s(t) = 5/2 t^2 for 0<=t<1 so, at t=1, s = 5/2 Now, using the 2nd function, s(t) = 5/2 + 4t^(3/2) - log(t) solve that for s(t) = 4
Sunday, March 23, 2014 at 8:21pm

Calculus
use implicit differentiation: x/2 + y/8 y' = 0 y' = -4x/y
Sunday, March 23, 2014 at 8:18pm

calculus
Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function: v(t)=5t if 0≤t<1 v(t)=6((t)^(1/2))-(1/t) if 1≤t where t is in seconds and v is in centimeters per second (cm/s). Estimate the time(s) at which the ...
Sunday, March 23, 2014 at 8:17pm

Calculus
Find the slope of the tangent line to the ellipse x^2/4 + y^2/16= 1 at the point (x,y)
Sunday, March 23, 2014 at 8:11pm

Calculus
the heat flow is proportional to the difference in temperature. dT/dt= -k(T-Tair) T air is a constant,
Sunday, March 23, 2014 at 7:24pm

Calculus
Suppose you have a hot cup of coffee in a room where the temp is 45 Celcius. Let y(t) represent the temp. of coffee as a function of the number of minutes t that have passed since the coffee was poured a) write a differential equation that applies to newtons law of cooling. ...
Sunday, March 23, 2014 at 6:16pm

CALCULUS ECONOMICS
How did you get to that number?I have 5000 (wrong solution) and I can't figure out q7 because i don't know the right value for q.opt (q.eq=625?)
Sunday, March 23, 2014 at 3:21pm

CALCULUS ECONOMICS
And for q7??It's my last chance...
Sunday, March 23, 2014 at 2:46pm

CALCULUS ECONOMICS
right for Q6!!!!!!!thankssssss
Sunday, March 23, 2014 at 2:26pm

CALCULUS ECONOMICS
2750? right or wrong?
Sunday, March 23, 2014 at 10:55am

CALCULUS ECONOMICS
Yes, they are right! Have you the answers of question 5,6,7? Thanks very very much!
Sunday, March 23, 2014 at 9:13am

CALCULUS ECONOMICS
Nothing?I need a clue in this one!
Sunday, March 23, 2014 at 6:54am

CALCULUS ECONOMICS
thanks
Sunday, March 23, 2014 at 4:55am

CALCULUS ECONOMICS
QUESTION: In this case, what is the difference between the optimal level of total consumption and the level of total consumption in equilibrium?
Sunday, March 23, 2014 at 4:18am

CALCULUS ECONOMICS
If Q = 440, shouldn't P = 560?
Sunday, March 23, 2014 at 1:55am

Calculus Help Please!!!
6x^2 + 9y^2 y' = 0 y' = -2x^2 / 3y^2 now for y", do it again: 12x + 18y (y')^2 + 9y^2 y" = 0 y" = -2(2x+3y(y')^2) / 3y^2 Now just substitute in y' and you're done Or, you can use the quotient rule on y': y' = -2/3 (x^2 / y^2) y&...
Saturday, March 22, 2014 at 4:02pm

Calculus Help Please!!!
find y' and y” by implicit differentiation. 2x^3 + 3y^3 = 8
Saturday, March 22, 2014 at 3:53pm

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